In known methods, solid impurities are removed from flush-back fluid drawn off from the flush-back filter by using flat material web filters, in particular endless paper band filters. In this respect, a flat material web filter is arranged over a collecting tank for flush-back fluid, which is dimensioned so as to be sufficiently large. Once it has been conveyed to the band filter, the flush-back fluid discharged from the flush-back filter passes through the filter material, and impurities are removed to a large extent from this fluid which then flows into the collecting tank while the separated impurities are transported into a separate disposal tank with the continuously or cyclically unrolling band filter. The flush-back fluid collecting in the collecting tank for the flush-back fluid is returned to the cleaning process or, if required, to the flush-back filter via a line comprising a pump. This results in the fluid being conveyed in a circuit. Methods of this type do, however, have the disadvantage that the resulting amounts of filter material are quite considerable and these have to be disposed of together with the impurities located thereon. In view of the necessarily large quantities of the cleaning fluid, which is primarily to be processed, flowing through the flush-back filter and in view of the pressure required at treating systems of the cleaning process, such as, for example, nozzles, the pressures prevailing in the interior of the flush-back filter are between 3 and 10 bars and so the discharge of flush-back fluid from the flush-back filter proves to be extremely problematic. On the one hand, the discharge opening provided in the flush-back filter would have to be as small as possible to limit the outflowing amount of flush-back fluid; on the other hand, the discharge opening would have to be designed sufficiently large in order not to become blocked. When using a discharge opening of small design or a throttle valve, there is, apart from the risk of clogging, the risk of the resulting strong stream of fluid damaging the flat material web filter. For this reason, in a known flush-back filter, a discharge line comprising a throttle valve opens into a steadying tank, which is of extremely large dimensions and from which the flush-back fluid loaded with impurities is then passed to the flat material web filter. An additional disadvantage of known processing methods is the fact that due to the partially open mode of operation considerable amounts of energy are lost by vaporization of the flush-back fluid originally used in the cleaning process as heated cleaning fluid as well as due to a necessarily poor insulation. An additional disadvantage is to be seen in the fact that in the known partially open mode of operation the surroundings are moistened to a considerable degree by evaporation and the escape of vapors and in this way chemical components are discharged into the environment.